creasing effective stress (by some combination of low-
point of thermodynamics was introduced. Thermodynam-
ering the water table and increasing the overburden
ic fundamentals and thermodynamic equilibrium con-
pressure) reduces the rate of frost heave of a soil, all
ditions are presented in the sections "Thermodynamic
other things being equal (Beskow 1935). Beskow incor-
fundamentals" and "Thermodynamic equilibrium,"
rectly concluded that frost heave rate in saturated soils
respectively. In "Thermodynamic treatment of frost
was independent of freezing rate, and his generalizations
heave," the modeling of frost heave based on equilib-
about frost heave were for a constant rate of freezing.
rium thermodynamics was briefly presented. In this sec-
Everett (1961) applied equilibrium concepts to
tion, a brief summary of the current understanding of
explain frost heave. He considered the mechanical equi-
frost heave, based on the work reviewed above, is pre-
librium between pore ice and pore water, thereby con-
sented without reference to any equations. This is
cluding that the maximum pressure difference in a heav-
intended to help readers better understand frost heav-
ing soil is determined by the smallest pore sizes. This
ing. It makes use of similarities between freezing and
was an important theoretical advancement; it provided
drying since most readers are more comfortable think-
a qualitative explanation for what is now known as pri-
ing about the evaporation of water from soils than about
mary frost heaving. However, he did not consider tem-
frost heave.
perature and chemical effects that can result in even
Drying is due to evaporation, or the conversion of
smaller radii of curvature between ice and water in soil
water to vapor by the addition of heat, whereas freez-
pores (leading to greater icewater pressure differences).
ing is the conversion of liquid to solid by the removal
Miller et al. (1960), Miller et al. (1975), and Loch
of heat. Conditions required for evaporation of water
(1978) developed a more complete thermodynamic equi-
from soil include 1) a supply of heat, 2) a means of
librium of pore ice and water; thus, chemical and ther-
transporting the vapor away from the pores, and 3) a
mal equilibrium are included. The Generalized Clapey-
supply of water. Conditions required for frost heave
ron Equation, based on the equilibrium of ice and water
include 1) a removal of heat, 2) a means of transport-
in soils is utilized by the thermodynamically based
ing the ice away from the pores (i.e., the ice lenses),
models of Miller (1978) and Gilpin (1980).
and 3) a supply of water. (Note, however, that the effec-
Miller (1978) and Gilpin (1980) used the equilibri-
tive stress must become zero in order for an ice lens to
um relationships as described by Loch (1978) and add-
initiate--this is discussed in detail later.)
ed heat and mass transfer in the frozen fringe to model
It may also be helpful to keep in mind the differences
frost heave. Darcy's Law and Fourier's Law describe
between the capillary fringe and the frozen fringe. The
heat and mass transfer in the frozen fringe, respectively,
capillary fringe is the soil just above the water table
and mass flow and heat flow are coupled by one equa-
where water rises up through capillary action. This layer
tion that describes heat transfer in the frozen soil. Ice
ranges in thickness from zero to a meter or so, and it
lenses start to grow when the effective stress in the fro-
depends on the pore sizes of the materials. In a soil that
zen fringe becomes zero (Miller 1978, Gilpin 1980).
frost heaves, recall that the frozen fringe is the soil just
The rigid ice model assumes that ice is one continuous
below the bottommost ice lens and above the unfrozen
rigid body that grows by regelation (Miller 1978).
soil where water and ice coexist in soil pores.
Gilpin's model also assumes that the ice forms a con-
Consider evaporation from soils. If the water in the
tinuous three-dimensional network, but it remains sta-
pores of the capillary fringe is in equilibrium with the
tionary in the frozen fringe. The main difference between
water vapor across curved liquid/vapor interfaces there
the models is that Gilpin made a few reasonable sim-
is no movement or phase change of water (i.e., no net
plifying assumptions that allowed the model to be pro-
evaporation). If water vapor is removed from the pores
grammed rather easily. However, more recent work with
by convection, for example, liquid water will change
the rigid ice model has made it relatively easy to use (e.g.,
phase to replace the vapor and water will flow up
Black 1995). Both models predict the same qualitative
through the soil pores to replenish the liquid water. If
frost heave behavior, and are similar quantitatively. The
the rate of water loss due to phase change is matched
rigid ice model is also the basis for the more recently
by the rate of water flow to replenish the liquid water,
developed numerical model used to predict frost heave
no change in the water distribution of the capillary fringe
in the field, known as PC heave (Sheng 1994).
occurs. If the soil at the location of phase change cannot
replenish the water for the given rate of heat addition,
(e.g., due to low hydraulic conductivity), the capillary
SUMMARY OF CURRENT UNDERSTANDING
fringe will increase in depth and/or thickness.
OF FROST HEAVE
Frost heave occurs by a process very similar to soil
In the introduction of this report the idea that the
freezing. In freezing soils, pore water is in equilibrium
frost heave of soils can be understood from the stand-
with ice across curved liquid/solid interfaces. However,
17
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